To offer a simple set of equations to designers and researchers for describing the degree of planarization (DOP), a first complete analytical solution of film planarization during spin coating is presented. The analytical solutions are suitable for an isolated feature and periodic features in the whole range of Omega(2). The governing dimensionless parameter Omega(2) represents the ratio of centrifugal force to surface tension force during spin coating. For Omega(2) --> 0, surface tension is infinite, and the film is planar. For Omega(2) --> infinity, surface tension is zero, and the film is always conformal, with an equal thickness everywhere. The analytical solutions agree with the existing experiment data and numerical solutions. A comparison shows that the degree of planarization for an isolated trench is higher than that for an isolated ridge in the range of 10(-5) < Omega(2) < 3 x 10(1), but they gradually become identical and independent of d/h(f) for Omega(2) > 3 x 10(1) and Omega(2) < 10(-5). For periodic features, DOPP is independent of dimensionless film thickness, d/h(f), dimensionless line spacing, alpha, and Omega(2) in the range of Omega(2) > 3 x 10(2) and Omega(2) <10(-2) (C) 1999 The Electrochemical Society. S0013-4651(99)01-014-9. All rights reserved.
